MPC is a control method which has been used in the chemical industry and, more recently, for load balancing and building energy management. The method uses real-time measurements, forecasted conditions and a model of a process. For a building energy management model, factors such as forecasted weather and past usage over time have been used as discussed in Oldewurtel, F., et al., “Use of model predictive control and weather forecasts for energy efficient building climate control,” Energy and Buildings, 45, 15-27 (2012) and in Cheung, J. Y. M., et al., “Model-based controllers for BEMS,” Industrial Applications of Model Based Predictive Control, IEE Colloquium, pp. 2/1, 2/6, Nov. 21, 1991 to predict future usage over a predefined time horizon in order to minimize energy usage, energy cost or peak energy consumption.
FIG. 1 shows a block diagram of an MPC system for building energy management. The system includes a fixed thermal model of the building and a controller. Based on the thermal model of the building, present temperature measurements and weather forecasts, the controller optimizes the building thermal performance over a fixed time interval that extends into the future. This optimization is achieved by proposing a large number of possible room temperature setpoints over the time horizon, then analyzing the resulting energy and temperature performance of the building based on the proposed setpoints, thermal model, and weather forecasts. Once this process is complete, the room temperature setpoints that minimize energy usage, cost or peak energy consumption over the interval are selected. The setpoints for the present time interval are implemented while the future setpoints are discarded, and in the next interval, the process is repeated with updated measurements.
Sophisticated models are available for modeling HVAC systems and thermal performance of buildings, but these are often too computationally intense for use in MPC where a large number of simulations must be performed in a short period of time. One commonly used model represents the building as an electrical circuit, for example where insulation between spaces like windows and walls act as thermal resistors, slowing down the flow of thermal energy between two spaces with different temperatures, and the air and objects in a room act as thermal capacitors, storing thermal energy and slowing down how quickly power raises the temperature of the room. In this model, temperature acts like voltage present at nodes within the system while current represents thermal energy flowing between nodes. Some nodes may operate at fixed temperatures, such as the measured outdoor temperature, while current sources may represent constant sources of thermal energy such as an electric heater.
FIG. 2 shows this thermal model. The current source, PSOURCE, represents the objects and people in the room that produce thermal power. This can include the HVAC system which regulates temperature in the room, a small space heater, human bodies, and electrical equipment like computers or refrigerators. The capacitor, CROOM, represents the heat capacity in the room. The air has a capacity to store heat power which changes based on humidity and total air volume, while objects in the room like furniture are also capable of storing heat power. The rate of change of temperature for a given input of thermal energy depends on the heat capacity of the room. The resistor, RINSULATION, represents the insulation between the room and outdoor space. The room may be connected to multiple other spaces and so may have multiple insulation resistors connecting it to each space. The value of this insulation depends on the material and thickness of the barriers between the room and the space. There may be multiple different barriers, such as a window within a wall. In this case each has a different insulation value and the equivalent insulation resistance between the spaces is an aggregate of the insulation resistances of these various barriers. Finally, the voltage source represents a fixed temperature. The outdoor temperature is dependent on its own set of complex factors, but it is measured directly and may be represented with a fixed parameter in this simulation. It changes slowly enough that it may be considered constant between measurement intervals.
The various components of this model change at various rates, resulting in significant error between the model's estimates of temperature and the actual temperature experienced in the building. Fux, S. F., et al., “EKF based self-adaptive thermal model for a passive house,” Energy and Buildings, 68, 811-817 (2014) and Ma, Yudong, et al., “Predictive Control for Energy Efficient Buildings with Thermal Storage,” IEEE Control Systems Magazine, 44-64, February 2012 both give methods of estimating this error. In the article by Fux et al., the expert engineer reviews the data and finds that there is significant error between the measured and estimated temperatures during scheduled meetings in the room. This error arises from adding several more heat energy sources, namely the people attending the meeting. This error is corrected manually, with a hard-coded script that adjusts the model during the scheduled meetings to account for the larger number of people in the room. This manual tweaking of the model represents one method of accounting for the errors that arise as the building changes. The weaknesses of this method are that it requires significant engineering investment from an expert and that the adjusted model immediately begins to become obsolete as soon as the expert leaves. Any changes in the occupant behavior, HVAC controls, or to the building structure will not be accounted for in the manually tuned model.
A second method to account for this error is presented in the article by Ma et al., where a Kalman filter is used to analyze data from a sample period and estimate the heat energy disturbance input. This estimated disturbance input is then included in the model, improving performance. In the article, the disturbance came when the occupants opened doors and windows, reducing the insulation between the interior rooms and the outdoors, but this method is able to provide a corrected disturbance input without needing to identify the source of the disturbance. This is an improvement over the first method in that it eliminates the need for an expert to review the data as well as speeding up the analysis, but the model still becomes obsolete as soon as circumstances change. It may be possible to automate this estimation, but the author does not provide a method for this.